Finite Group DatabasebetaFinite Group DatabasebetaOrder 36224.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q8×Dic283 | C2 | semidirect |
| 3. #31826779 | C2 | semidirect |
| 4. #31826776 | C2 | semidirect |
| 5. #31826758 | C2 | semidirect |
| 6. #31826663 | C2 | semidirect |
| 7. #31826604 | C2 | semidirect |
| 8. #31826568 | C2 | semidirect |
| 9. #31826566 | C2 | semidirect |
| 10. #31826519 | C2 | semidirect |
| 11. #448×C283 | C2 | semidirect |
| 104. Q8×C283 | #41 | semidirect |
| 140. C283 | #3112 | semidirect |
| 149. #448 | D283 | semidirect |
| 229. Q8 | #17985391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31827010 | 2 |
| C2×Q8×Dic283 | 2 |
| #31826779 | 2 |
| #31826776 | 2 |
| #31826758 | 2 |
| #31826663 | 2 |
| #31826604 | 2 |
| #31826568 | 2 |
| #31826566 | 2 |
| #31826519 | 2 |
| #448×C283 | 2 |
| #3112 | 283 |